B.1. Hypoglycemia in Diabetes
Hypoglycemia is common in Type 1 Diabetes Mellitus (T1DM) [24] and becomes more prevalent in Type 2 Diabetes Mellitus (T2DM) with treatment intensification [7]. Hypoglycemia-associated autonomic failure (HAAF) is well documented in T1DM [4] and is observed in intensively treated T2DM as well [22]. Even state-of-the-art therapies are imperfect and may trigger acute lowering of blood glucose (BG) levels, potentially leading to severe hypoglycemia (SH), defined as severe neuroglycopenia resulting in unconsciousness or stupor that precludes self-treatment [24]. SH may cause cognitive dysfunction, coma, or sudden death [6, 24]. Consequently, hypoglycemia has been identified as the primary barrier to optimal diabetes management [3].
B.2. Potential Predictors of Hypoglycemia
Glycosylated hemoglobin (HbA1c) is the classic marker of glycemic status, introduced 23 years ago [1], linked to diabetes complications, and confirmed as the gold standard measure of average glycemic control in T1DM and T2DM, [20, 25, 27]. However, in addition to establishing HbA1c, the Diabetes Control and Complications Trial (DCCT) concluded that: “HbA1c is not the most complete expression of the degree of glycemia. Other features of diabetic glucose control, which are not reflected by HbA1c, may add to, or modify the risk of complications. For example, the risk of complications may be more highly dependent on the extent of postprandial glycemic excursions” [26]. Consequently, contemporary studies increasingly concentrate on the variability of BG fluctuations as an independent factor for diabetes complications [2]. The two most prominent manifestations of glycemic variability are hypoglycemia and postprandial glucose (PPG) elevation.
Standard Deviation and Other Variability Measures:
The traditional statistical calculation of BG variability includes computing the standard deviation (SD) of BG readings as well as several other measures: (i) The M-value introduced in 1965 [21]; (ii) MAGE—Mean Amplitude of Glucose Excursions—introduced in 1970 [23], and (iii) the Lability Index (LI)—a recently developed measure of hypoglycemia and glycemic lability [19]. Most of these measures (except the LI) have a relatively weak association with hypoglycemia and an inherent bias towards hyperglycemia, which is reflected by the historically poor prediction of SH [24]. In previous studies, we have found that the basis for that poor prediction appeared to be mathematical, rather than clinical: it lies in the fact that the BG measurement scale is asymmetric and substantially skewed towards hyperglycemia [13]. Thus, clinical conclusions based on numerical methods, will be less accurate for the constricted hypoglycemic range and will be biased towards hyperglycemia.
B.3. Risk Analysis of BG Data
In order to correct the numerical problem created by the asymmetry of the BG scale we have introduced a mathematical transformation that symmetrizes the BG scale [13]. It is important to note that the analytical form of this transformation is based on accepted clinical assumptions, not on a particular data set, and has been fixed ten years ago [13], which makes the approach extendable to any data set. Based on this transformation, we have developed our theory of risk analysis of BG data [12, 15, 8] that defines a computational risk space that proved to be very suitable for quantifying the extent and frequency of glucose excursions. In essence, analysis in risk space entails converting first each BG reading into a risk value using two simple steps: (i) application of the symmetrization formula [13], and (ii) application of a quadratic risk function that assigns increasing weights to larger BG deviations towards hypoglycemia or hyperglycemia [18]. In brief, the BG measurement scale is numerically asymmetric—the hyperglycemic range (180 to 600 mg/dl) is much greater that the hypoglycemic range (20-70 mg/dl) and the euglycemic range (70-180 mg/dl) is not centered within the scale. We have corrected this asymmetry by introducing a transformation f(BG)—a continuous function defined on the BG range [20, 600] that has the general two-parameter analytical form [13]:f(BG,α,β)=[(ln(BG))α−β],α,β>0and satisfies the assumptions:f(600,α,β)=−f(20,α,β) and  A1:f(180,α,β)=−f(70,α,β).  A2:
By multiplying by a third parameter γ we fix the minimal and maximal values of the transformed BG range at −√{square root over (1)}0 and √{square root over (1)}0 respectively. When solved numerically under the restriction α>0, these equations give: α=1.084, β=5.381, γ=1.509. These parameters are sample-independent and have been fixed in 1997 [13].
After fixing the parameters off(BG) depending on the measurement scale that is being used, we define the quadratic function r(BG)=10f(BG)2, which defines the BG Risk Space. The function r(BG) ranges from 0 to 100. Its minimum value is 0 and is achieved at BG=112.5 mg/dl, a safe euglycemic BG reading, while its maximum is reached at the extreme ends of the BG scale (20 mg/dl and 600 mg/dl). Thus, r(BG) can be interpreted as a measure of the risk associated with a certain BG level. The left branch of this parabola identifies the risk of hypoglycemia, while the right branch identifies the risk of hyperglycemia. These branches are identified by the formulas [18]:rl(BG)=r(BG) if f(BG)<0 and 0 otherwise (left branch);  (1)rh(BG)=r(BG) if f(BG)>0 and 0 otherwise (right branch).  (2)
The Low BG Index (LBGI): is based on the left branch of the BG Risk Function (BG) and accounts for the frequency and extent of hypoglycemia. The LBGI has been validated by multiple studies as an excellent predictor of future significant hypoglycemia [10, 11, 12, 14, 15]. The LBGI also provides means for classification of the subjects with regard to their long-term risk for hypoglycemia into: Minimal, Low, Moderate and High-risk groups, with LBGI of below 1.1, 1.1-2.5, 2.5-5.0, and above 5.0 respectively [15], and has been used for short term prediction of hypoglycemia as well [5, 9]. By definition, the LBGI is independent from hyperglycemic episodes.
The Average Daily Risk Range (ADRR) is a measure of glycemic variability based on both rl(BG) and rh(BG), which has been shown superior to traditional measures in terms of risk assessment and prediction of extreme glycemic excursions [16,17]. Specifically, it has been demonstrated that classification of risk for hypoglycemia based on four ADRR categories: Low Risk: ADRR <20; Low-Moderate Risk: 20≤ADRR<30; Moderate-High Risk: 30≤ADRR<40, and High Risk: ADRR>40, results in an over six-fold increase in risk for hypoglycemia from the lowest to the highest risk category [17].